Theorem orim2d 800

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 798	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

This proof depends on syntax axioms:   -> wi 4   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  orim2  801  orbi2d  802  pm2.82  824  stdcndcOLD  858  pm2.13dc  897  exmid1dc  4337  acexmidlemcase  6080  poxp  6468  fodjuomnilemdc  7484  omniwomnimkv  7507  exmidontriimlem1  7577  indpi  7709  suplocexprlemloc  8088  nneoor  9752  uzp1  9965  maxabslemlub  11988  xrmaxiflemlub  12030  nninfctlemfo  12833  exmidunben  13366  bj-nn0suc  17088  sbthomlem  17168